DPLL algorithm:

\begin{tabular}{|l|c|c|c|c|c|}
\hline
Step                        & 1 & 2       & 3         & 4         & 5         \\ \hline \hline
Decision Level              & 0 & 0       & 0         & 0         & 0         \\ \hline
Assignment                  & - & $\lnot a$     & $\lnot a,\lnot b$     & $\lnot a,\lnot b,\lnot c$   & $\lnot a,\lnot b,\lnot c,\lnot d$ \\ \hline
Cl. 1: $\lnot a, b$         & 1 & \cmark     & \cmark    & \cmark    & \cmark    \\ \hline
Cl. 2: $\lnot b, c$         & 2 & 2       & \cmark       & \cmark    & \cmark    \\ \hline
Cl. 3: $\lnot c, d$         & 3 & 3       & 3         & \cmark       & \cmark    \\ \hline
Cl. 4: $\lnot d, e$         & 4 & 4       & 4         & 4         & \cmark       \\ \hline
Cl. 5: $\lnot e, \lnot a$   & 5 &\cmark& \cmark & \cmark& \cmark\\ \hline \hline
BCP                         & -  &  -    &     -   &    -    &   -    \\ \hline
PL                          & $\lnot a$  & $\lnot b$     & $\lnot c$       &  $\lnot d$      &  -    \\ \hline
Decision                    & - &   -     &    -      &   -       & SAT          \\ \hline
\end{tabular}

Model:

$a$ = F, $b$ = F, $c$ = F, $d$ = F, $e$ = F